(A) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten
expansion of 2P is equal to P-1.

(B) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten expansion of 6P is equal to P-1.

It turns out I encountered a flaw in the way it finds the intersection of two functions. The first-two-digits function has discontinuities similar to a greatest integer function. P-1 passes through most of these gaps. Whatever variation of Newtons method it uses, sometimes things just go wrong in these cases. Instead of reporting no solution it reported a solution that isnt even very close.

Yesterday, I though I was going to get solutions like 2^13.55075 = 12000.026738460294. I will leave it at this. This could make a nice extension of the problem.